Slow/beginners' sessions at festivals are great. Some regular sessions spend the first part of the session either teaching tunes or playing them slowly(I know of a few in Derbyshire so contact me if you are interested).

Something nobody has mentioned thus far is to record tunes at session that you usually attend when they play them too fast for you to join in. This is something I found very useful. Then, you can take them home and learn them at your leisure. Play them in the car and learn to hum them. Once the tune is in your head, you'll know if you're playing it correctly.

Hope this helps

Sylvia